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arXiv · 1304.3884

Spin structures on 3-manifolds via arbitrary triangulations

Riccardo Benedetti·Carlo Petronio
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Abstract

Let M be an oriented compact 3-manifold and let T be a (loose) triangulation of M, with ideal vertices at the components of the boundary of M and possibly internal vertices. We show that any spin structure s on M can be encoded by extra combinatorial structures on T. We then analyze how to change these extra structures on T, and T itself, without changing s, thereby getting a combinatorial realization, in the usual "objects/moves" sense, of the set of all pairs (M,s). Our moves have a local nature, except one, that has a global flavour but is explicitly described anyway. We also provide an alternative approach where the global move is replaced by simultaneous local ones.

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Riccardo Benedetti, Carlo Petronio. 2013-04-14. Spin structures on 3-manifolds via arbitrary triangulations. https://doi.org/10.2140/agt.2014.14.1005

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